Thermodynamic relations

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Notation used:

These thermodynamic relations are also known as coefficient relations.

T=\left(\frac{\partial U}{\partial S}\right)_V

 p=-\left(\frac{\partial U}{\partial V}\right)_S

T=\left(\frac{\partial H}{\partial S}\right)_p

 V=\left(\frac{\partial H}{\partial p}\right)_S

S=-\left(\frac{\partial A}{\partial T}\right)_V

 p=-\left(\frac{\partial A}{\partial V}\right)_T


 S=-\left(\frac{\partial G}{\partial T}\right)_p

 V=\left(\frac{\partial G}{\partial p}\right)_T

See also[edit]